Applied Functional Analysis. Approximation Methods and Computers: Applied Functional Analysis, Approximation Methods and Computers

ISBN-13: 9782884490139 / Angielski / Twarda / 1996 / 400 str.

S.S. Kutateladze;S.S. Kutateladze

Opis

Kantorovich, the late Nobel Laureate, was a respected mathematical economist, and one of the founding fathers of linear programming. Part I begins with chapters on the theory of sets and real functions. Topics treated include universal functions, W.H. Young's classification, generalized derivatives of continuous functions and the H. Steinhaus problem. The book also includes papers on the theory of projective sets, general and particular methods of the extension of Hilbert space, and linear semi-ordered spaces. The author deals with a number of approximate calculations and solutions including a discussion of an approximate calculation of certain types of definite integrals, and also a method for the approximate solution of partial differential equations. In addition to this, the author looks at various other methods, including the Ritz method, the Galerkin method in relation to the reduction of differential equations and the Newton methods for functional equations. Towards the end of the book there are several chapters on computers.

Spis treści

1. On convergence of the sequence of Bernstein polynomials beyond the principal interval 2. Some remarks on approximation of functions by polynomials with integer coefficients 3. On certain expansions in Bernstein polynomials 4. Explicit representation of a measurable function as the limit of polynomial sequences 5. A direct method for approximate solution of the problem of a double integral minimum 6. On conformal mappings 7. Application of the Stieltjes integral to the calculation of beams lying on elastic supports 8. On approximate calculation of certain types of definite integrals 9. On general methods of improving the convergence for approximate solutions to boundary value problems of mathematical physics 10. On a method of approximate solution of partial differential equations 11. On convergence of variational processes 12. On the convergence of the method of reduction to ordinary differential equations 13. Some remarks on the Ritz method 14. Using the ideas of the Galerkin method in the method of reduction to differential equations 15. On an effective method of solving extremal problems for quadratic functionals 16. On the method of steepest descent 17. On Newton’s method for functional equations 18. Functional analysis and applied mathematics 19. On differential equations of the form xn=f(x) 20. On the Newton Method 21. Some further applications of the Newton method for functional equations 22. New modes of calculations with the tabulator using the binary representations of numbers 23. Prospects in the development and applications of computers 24. Execution of numeric and analytic calculations on computers 25. Increasing of productivity of universal computers in solving problems of mathematical economics

O autorze

S.S. Kutateladze